WASHINGTON — The health care law has opened up an unusual opportunity for some mothers-to-be to save on medical bills for childbirth.

Lower-income women who signed up for a private policy in the new insurance exchanges will have access to additional coverage from their state’s Medicaid program if they get pregnant. Some women could save hundreds of dollars on their share of hospital and doctor bills.

Medicaid already pays for nearly half of U.S. births, but this would create a way for the safety-net program to supplement private insurance for many expectant mothers.

Officials and advocates say the enhanced coverage will be available across the country, whether or not a state expands Medicaid under the health law. However, states have different income cutoffs for eligibility, ranging from near the poverty line to solid middle class.

The main roadblock seems to be logistical: reprogramming state and federal computer systems to recognize that certain pregnant women have a legal right to coverage both from Medicaid and private plans on the insurance exchange. Technically, they can pick one or the other, or a combination.

States and insurers will have to sort out who pays for what.

Another big challenge will be educating the public about this latest health law wrinkle. It’s complicated for officials and policy experts, let alone the average consumer.

“This is an issue where women are going to have to figure out, ‘I’m eligible for both, now how do I do that?’ ” said Matt Salo, executive director of the National Association of Medicaid Directors, which represents state programs. “But what a wonderful problem to have. This is a great problem to have from the consumer’s perspective.”

The cost impact for federal and state taxpayers is uncertain. Providing more generous coverage increases costs, but comprehensive prenatal care can save money by preventing premature births and birth defects.

Cynthia Pellegrini, head of the March of Dimes’ Washington office, said many women might not have been thinking about maternity benefits when they signed up for coverage under the health law. After all, half of U.S. pregnancies are unplanned. Often consumers focus on the monthly premium when they select a plan.

The cost of normal uncomplicated childbirth averages $5,000, said Pellegrini, and preterm births can cost more than 10 times that. Co-payments and deductibles add up fast.